含扩散项不可靠生产系统最优生产控制的数值求解

针对含扩散项不可靠随机生产系统最优生产控制的优化命题, 采用数值解方法来求解该优化命题最优控制所满足的模态耦合的非线性偏微分HJB方程. 首先构造Markov链来近似生产系统状态演化, 并基于局部一致性原理, 把求解连续时间随机控制问题转化为求解离散时间的Markov决策过程问题, 然后采用数值迭代和策略迭代算法来实现最优控制数值求解过程. 文末仿真结果验证了该方法的正确性和有效性.

Numerical solution for optimal production control of unreliable production systems with diffusion terms

The optimal production control for unreliable stochastic production system always involves in solving a mode-coupled nonlinear partial differential equation, i.e., HJB(Hamilton-Jacobi-Bellman) equation, which is the necessary and sufficient condition of optimal control. Numerical method for stochastic control problems in continuous time is adopted to solve the optimal production control problem involving diffusion terms by constructing Markov chains to approximate the evolution of the system states, and then, the associated HJB equation is transformed into a discrete time Markov decision process(MDP) under local consistence. Based on the MDP, an algorithm including numerical iteration and policy iteration is then proposed. Finally, some numerical examples of production system are presented to illustrate the usefulness of the numerical method.